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Question

Three rods made of the same material and having the same cross section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at 0 to the power of o end exponent C and 9 0 to the power of o end exponent C respectively. The temperature of the junction of the three rods will be

  1. 4 5 to the power of o end exponent C    
  2. 6 0 to the power of o end exponent C    
  3. 3 0 to the power of o end exponent C    
  4. 2 0 to the power of o end exponent C    

The correct answer is: 6 0 to the power of o end exponent C


    Let the temperature of junction be q. Since roads B and C are parallel to each other (because both having the same temperature difference). Hence given figure can be redrawn as follows

    Q fraction numerator Q over denominator t end fraction equals fraction numerator left parenthesis theta subscript 1 end subscript minus theta subscript 2 end subscript right parenthesis over denominator R end fraction and open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript A B end subscript equals open parentheses fraction numerator Q over denominator t end fraction close parentheses subscript B C end subscript
    Þ fraction numerator left parenthesis 90 minus theta right parenthesis over denominator R divided by 2 end fraction equals fraction numerator left parenthesis theta minus 0 right parenthesis over denominator R end fraction Þ 180 minus 2 theta equals theta Þtheta equals 60 degree C

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